Is zakat obligatory on the sum of 190,000 pounds that was invested in a rental apartment, and is it obligatory on the principal amount or on the principal and profit combined?

If your mother's money is invested in a legitimate mudarabah (definition) (profit-sharing) venture, then it is subject to zakat (definition) as trade goods when a hawl (lunar year) passes and it reaches the nisab (definition) (minimum threshold). The monthly profit is added to the principal capital, and all of it is subject to zakat at once, because the hawl for the profit is the same as the hawl for its principal. However, if your mother spends this profit on rent and expenses, then there is no zakat due on it.